Which seems to imply that taking \(\lim n \rightarrow 1\) , \(S_R(A:B) = 0\)  for \(x_A + x_B > 1\)  which cannot be the case. In particular it violates the mutual information bound \(S_R \ge I\) . Previously this was attributed to an order of limits issue [1]} where one must take \(\lim _{m \rightarrow 1} \lim _{n \rightarrow 1}\)  to get the right answer - indeed here that resolution does work. However this result gives a very puzzling set of Rényi entropies, which were naively still consistent. However we can now observe using Lemma REF  that they are in fact not consistent, since for \(m = 2\) , we see that either \(F(X)=F(e)\)  or \(F(g_{A,B})\)  dominates and neither gives the same reflected entropy as the naive \(m=1\)  phase with \(g=e\)  given in naivee. This is inconsistent with the continuity bounds of Lemma REF , at least in some window of parameters.
